Dynamics analysis and control optimization of a pest management predator-prey model with an integrated control strategy

This work presents a new integrated pest management predator-prey model.It has shown the existence of the order-1 periodic orbit for the proposed model.It has verified the stability of the order-1 periodic orbit by geometric method.It has obtained optimal pest control level by an optimization problem. Pest management is a complex issue in real applications, and a practical program in pest control in general involves two pest thresholds, where the biological control and chemical control are activated respectively. Aiming at providing a good balance between the biological control and chemical control, this work presented an integrated pest management predator-prey model, where the yield of releases of predator and the strength of pesticide spraying are linearly dependent on the selected control level. Firstly, to determine the frequency of spraying chemical pesticide and releasing of predator, the existence of the order-1 periodic orbit of the proposed model is discussed by the successor function method. And then, to ensure a certain robustness of adopted control, the stability of the order-1 periodic orbit is verified by a stability criterion extracted for a general semi-continuous dynamical system. In addition, to minimize the total cost (i.e. culturing predators and spraying pesticide) in pest control, an optimization problem is formulated and the optimum pest control level is obtained. At last, to complement the theoretical results, the numerical simulations with a specific model are carried out step by step.